def __init__(self, p=None, q=None, a=None, b = None, n=None, nb_bits=4096):
"""Initializes the magic keys.
"""
if p is None and q is None and a is None:
# 1. Generates 'p' and 'q' prime numbers of lengths 'nb_bits' in a
# random fashion.
if p is None and q is None:
p = random.getrandbits(nb_bits)
q = random.getrandbits(nb_bits)
while not utils.miller_rabin(p):
p = random.getrandbits(nb_bits)
while not utils.miller_rabin(q):
q = random.getrandbits(nb_bits)
if a is None and b is None and n is None:
# 2. Generates 'a', 'b' and 'n' thanks to 'phi' and 'b'.
n = p * q
phi = (p - 1) * (q - 1)
if b is None:
while True:
b = random.randint(2, phi - 1)
if utils.is_prime_together(b, phi):
break
a = utils.inv_modulo(b, phi)
self.private = a
self.public = b
self.modulus = n
def dfs(rem, s, prev):
if len(rem) == 0 and s == 0:
return 1
cnt = 0
for d in rem:
next_s = s * 10 + d
if next_s > prev and utils.miller_rabin(next_s):
cnt += dfs(rem - set([d]), 0, next_s)
cnt += dfs(rem - set([d]), next_s, prev)
return cnt
def dfs(d, flag, cur, i):
if (i == N):
if utils.miller_rabin(cur):
return cur
return 0
if flag[i]:
return dfs(d, flag, cur * 10 + d, i + 1)
s = 1 if i == 0 else 0
ret = 0
for k in range(s, 10):
ret += dfs(d, flag, cur * 10 + k, i + 1)
return ret
def count(n, n_list):
return sum(utils.miller_rabin(abs(n - e)) for e in n_list)
"""
import utils
SUP = 100000
def cycle_len(mod):
rems = set()
n = 1
while n not in rems:
rems.add(n)
n = (n * 10 + 1) % mod
return len(rems)
def check(n):
while n % 2 == 0:
n //= 2
while n % 5 == 0:
n //= 5
return n == 1
ans = 0
for i in range(2, SUP):
if utils.miller_rabin(i):
if i == 2 or i == 5 or not check(cycle_len(i)):
ans += i
print(ans)
def check(p, q):
return utils.miller_rabin(numcat(p, q)) and utils.miller_rabin(numcat(q, p))
# -*- coding: utf-8 -*-
"""
Created on Wed Apr 18 14:01:45 2018
@author: lamwa
"""
import utils
SUP = 10 ** 6
ans = 0
a = 1
while True:
p = (a + 1) ** 3 - a ** 3
if p >= SUP:
break
if utils.miller_rabin(p):
ans += 1
a += 1
print(ans)
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 21 13:57:20 2018
@author: lamwa
"""
import utils
cur = 0
cnt = 1
n = 1
while True:
if utils.miller_rabin(4 * n * n - 2 * n + 1):
cur += 1
if utils.miller_rabin(4 * n * n + 1):
cur += 1
if utils.miller_rabin(4 * n * n + 2 * n + 1):
cur += 1
if utils.miller_rabin(4 * n * n + 4 * n + 1):
cur += 1
cnt += 4
if cur / cnt < 0.1:
print(n * 2 + 1)
break
n += 1
# -*- coding: utf-8 -*-
"""
Created on Mon Apr 25 16:11:11 2018
@author: lamwa
"""
import utils
SUP = 150000000
ans = 0
for n in range(10, SUP, 10):
if n % 1000000 == 0:
print(n)
s = n * n
if (s % 3 != 1): continue
if (s % 7 != 2 and s % 7 != 3): continue
if (s % 9 == 0 or s % 13 == 0 or s % 27 == 0): continue
if ( utils.miller_rabin(s + 1) and \
utils.miller_rabin(s + 3) and \
utils.miller_rabin(s + 7) and \
utils.miller_rabin(s + 9) and \
utils.miller_rabin(s + 13) and \
not utils.miller_rabin(s + 19) and \
not utils.miller_rabin(s + 21) and \
utils.miller_rabin(s + 27)):
ans += n
print(ans)